SQL Server 2016 – How to Remove Read-Only Routing URL

You are attempting to connect to databases on secondary replicas when the availabilty group replica is not configured to allow connections on anything other than the primary replica.

The following script will tell you the state of the secondary replicas, and whether they will accept read connections:

SELECT ag.name,
       replica_server_name,
       secondary_role_allow_connections_desc
FROM sys.availability_replicas ar
    JOIN sys.availability_groups ag
        ON ag.group_id = ar.group_id;

The result of each replica with be:

• NO - no connections allowed to the database (default behavior)
• READ_ONLY - connections allowed when the ReadIntent flag is passed in a connection string
• ALL - all connections to the databases are permitted.

To change the setting for a replica you can either use the GUI, or a script:

ALTER AVAILABILITY GROUP [AGName]
MODIFY REPLICA ON 'ReplicaName'
WITH (SECONDARY_ROLE (ALLOW_CONNECTIONS = ALL, READ_ONLY_ROUTING_URL = 'TCP://ReplicaName:Port'))

For more details see the Microsoft documentation.

What do you suggest on above ?

I need to keep primary SQL server replica as 2012 for now, and I need to make >async replica (SQL server 2016) to be available for read-only access

There is nothing you can do, this is a known item:

During a version upgrade, readable secondaries cannot be read after an upgrade of the readable secondary and before either the primary replica is failed over to an upgraded secondary or the primary replica is upgraded.

https://docs.microsoft.com/en-us/sql/database-engine/availability-groups/windows/upgrading-always-on-availability-group-replica-instances